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The time-dependent von Kármán plate equation as a limit of 3D nonlinear elasticity

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Abels, Helmut ; Mora, Maria Giovanna ; Müller, Stefan
Date of publication of this fulltext: 12 Feb 2010 09:43


The asymptotic behaviour of the solutions of three-dimensional
nonlinear elastodynamics in a thin plate is studied, as the thickness h of the
plate tends to zero. Under appropriate scalings of the applied force and of the
initial values in terms of h, it is shown that three-dimensional solutions of the
nonlinear elastodynamic equation converge to solutions of the time-dependent
von Kármán plate equation.

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